[ 08 ]lab · simulations

Beam deflection and stress

Cantilever, simply-supported or fixed-fixed, a point or uniform load, four cross-sections and six material presets. The deflected shape and the bending moment diagram come from the same deflection curve, so they can never disagree with each other.

lab · sims · beam deflection

PID tuner →Rise time, overshoot, settling time. Motion planner →Trapezoidal and S-curve stepper moves. RC/RLC filter →Bode plot and step response.

The beam [ live ]

deflected shape, exaggerated —

bending moment diagram

—max deflection

—max bending moment

—max bending stress

—safety factor

—material strength used

Support & load

support load span L (mm) point load P (N) load position a (mm) uniform load w (N/mm)

Section

shape

width b (mm) height h (mm)

Material

preset override E (GPa, optional)

Assumptions and limits. Linear-elastic, small-deflection (Euler-Bernoulli) beam theory - no buckling check, no shear deflection, and the point load's own weight is ignored next to the applied load. The bending moment is not an independently-typed formula: it is EI times the second derivative of the plotted deflection curve, taken numerically, so the two plots are guaranteed consistent with each other even if a moment sign convention was fumbled somewhere else. Printed materials are shown for the in-plane direction only - a layer-adhesion (Z) load is commonly a third or less of that strength, which this model does not represent. Deflection is checked against the textbook closed forms for a cantilever end load (δ=PL³/3EI) and a simply-supported central load (δ=PL³/48EI) in the test suite.